When you first spawn in the Wharf District, pick up the bow. Then follow the wooden walkways forward, using a ranged weapon to destroy the turrets, and your hammer to kill any close up enemies and to clear a path.
You will reach the distillery and arsenal. Walk past these to find more wooden walkways. At the end of this, you will come to 2 paths. Take the one on the right (your character's left) and hit the switch. The barge wiil start moving, and you will have turrets and various other enemies to kill.
At the top, when the barge stops, pick up the 'Something Heavy' in the middle. 2 big blueberry enemies and a large hooded figure will appear. Destroy the two carts at the top right of the screen dispensing the small, dark blue enemies (Squirts) using your whirlwind ability (RT). Kill the blueberries (scumbags) one at a time, using A to dodge their blue sludge attacks. After each dodge hit them a few times with your hammer, but don't get greedy. Do the same for the large hooded figure.
Pick up all the loot that drops after they are dead, then head through the gate that opens up at the top right of the screen.
Walk on a bit and pick up the blue glowing 'core'. After this, the gate ahead will open. You must hurry in this section, as the path will start to fall away. There will be quite a few enemies, but just kill the ones that get in your way. All the paths lead to the same place, and you will eventually come to the end, where you have to press X to warp to the Skyway, which ends the level.